Coherence time is the single most important hardware constraint on what quantum circuits are tractable before errors accumulate unacceptably. It deserves careful reporting, which means fully specified protocols, honest error budgets, and a clear statement of what was held fixed when numbers were measured. This post presents our current T1 and T2 measurements from the 100-atom strontium-88 platform, with sufficient protocol detail to allow comparison against other reported results.
Measurement protocol for T1
T1 characterizes energy relaxation: how long a population-inverted qubit stays in the excited state before returning to the ground state via spontaneous emission or phonon exchange. We measure T1 using a straightforward inversion-recovery sequence. A pi pulse prepared by the clock laser at 698 nm inverts the ground state population into the metastable 3P0 state. We then wait a variable delay and apply a projective measurement.
Delays are logarithmically spaced between 10 ms and 8 seconds, giving 20 points that adequately sample the decay. At each delay point, the sequence is repeated 200 times, with atom loading and cooling performed fresh for each repetition to avoid accumulated preparation errors. The population decay is fit to a single exponential, and T1 is the extracted decay constant. A full T1 measurement for a single site takes approximately 12 minutes. We report T1 averaged across all 100 sites, with the site-to-site distribution discussed separately.
Measurement protocol for T2
T2 is the phase coherence time, which is typically shorter than T1 and more directly relevant to gate performance. We measure T2 using a Ramsey sequence: two pi/2 pulses with a variable free evolution period between them. Without any additional pulse sequence between the two pi/2 pulses, we measure T2*. With a dynamical decoupling sequence interpolated during the free evolution period, we measure T2 under decoupling (T2,DD).
For T2,DD we use the XY-8 dynamical decoupling sequence, which applies 8 pi pulses in alternating X and Y rotation axes during the free evolution period. XY-8 is effective at refocusing low-frequency magnetic field noise and laser frequency noise below roughly 10 kHz, which are the dominant broadening mechanisms in our system. We apply XY-8 as our standard operating mode in all science experiments, so T2,DD is the more practically relevant figure.
T2 Ramsey curves show oscillations at the qubit detuning frequency, and we fit the envelope of these oscillations to extract the coherence time. At long delays, the oscillation amplitude decays following an approximately Gaussian envelope in our system, consistent with quasi-static noise that is slowly fluctuating on the timescale of the repetition rate. We use a Gaussian decay model for the fit rather than an exponential, which would systematically overestimate T2 in this regime.
Results
Measured T1 (median across all 100 sites): 4.3 seconds, standard error 0.2 s, from 50 independent measurement runs distributed across two weeks of operation in May 2026. The site-to-site distribution is reasonably tight, with 90% of sites falling between 3.6 and 4.9 seconds. The outliers on the low end are sites near the array edge where trap depth is lower due to the Gaussian beam envelope.
Measured T2,DD (median, XY-8 with 8 pulses): 1.1 seconds, standard error 0.08 s. T2* (no decoupling) averages 180 ms, with considerable site-to-site variation. The ratio T2,DD / T2* of approximately 6 indicates that the decoupling is recovering a substantial fraction of phase coherence lost to low-frequency noise, which is consistent with the noise spectrum of our clock laser cavity.
These values represent a 30% improvement over our Q3 2025 baseline of T1 = 3.3 s and T2,DD = 0.85 s. The improvement is attributable primarily to two hardware changes implemented in early 2026: active magnetic field shielding using a mu-metal enclosure around the experimental region, and vibration isolation stacks added under the optical table. The shielding reduced the low-frequency magnetic field noise by approximately a factor of 4, as measured by a magnetometer placed at the atom position.
What limits coherence at this scale
The current limiting factor for T2,DD is residual low-frequency laser frequency noise below 1 Hz that the XY-8 sequence cannot fully refocus. This noise originates in thermal fluctuations in the ULE cavity used as the clock laser frequency reference. The noise floor at sub-1 Hz frequencies is set by Brownian motion in the cavity spacer and mirrors, which scales roughly as 1/f^0.5. We have verified this attribution by temporarily switching to a different reference cavity with a better low-frequency noise floor and observing a proportional T2,DD improvement.
The path forward is either a cryogenic silicon cavity, which has a fundamentally lower thermal noise floor, or a longer XY-n sequence with more pi pulses to push the decoupling bandwidth to lower frequencies. The cryogenic cavity option has better long-term coherence prospects but adds substantial infrastructure complexity. We are currently testing an XY-32 sequence, which extends the noise rejection bandwidth by a factor of 4 relative to XY-8 at the cost of longer state preparation overhead and more laser pulse errors that accumulate over the additional pi pulses.
T1, by contrast, is not currently limiting anything. With a 100 ns typical two-qubit gate time and T1 of 4.3 seconds, the T1 contribution to per-gate error for a gate sequence is approximately 2 x 10^-5 per gate. Two-qubit gate error rates are currently measured at roughly 0.5% to 1%, so T1 error is three orders of magnitude below the gate error floor. We mention this not to claim the T1 numbers do not matter, but to be honest that chasing better T1 on the current system would not move the needle on achievable circuit depth.
Reporting conventions and comparisons
When comparing coherence times across platforms, the reporting conventions matter as much as the numbers. T2* numbers without specifying the broadening mechanism are not useful for comparison. T2 under a specified decoupling sequence is more informative but depends on the sequence length and pulse count. And neither T2 number translates directly to circuit performance without knowing the gate time, which sets the ratio of circuit duration to coherence time.
For our platform: with a typical single-qubit gate time of 5 microseconds and a two-qubit gate time of 200-400 microseconds, the relevant figure of merit is T2,DD / t_gate. For single-qubit gates this is approximately 220,000, meaning a coherence-limited single-qubit error rate of around 4 x 10^-6. For two-qubit gates the ratio is approximately 4,000, giving a coherence-limited two-qubit error rate of around 2.5 x 10^-4, which is well below current two-qubit gate error rates. In both cases, coherence is not the practical limit. Gates are. That is where our engineering attention is focused.